I couldn't find any information on the tech in the article or the future meat site but the founder's lab site has some pretty good hints in his publication list. https://www.nahmias-lab.com/publications
G. Levy, D. Bomze, S. Heinz, S.D. Ramachandran, A. Noerenberg, M. Cohen, O. Shibolet, E. Sklan, J. Braspenning, Y. Nahmias. Long-term culture and expansion of primary human hepatocytes. Nature Biotechnology 33(12): 1264-1271. (2015)
Y. Nahmias, D. J. Odde, Micropatterning of living cells by laser-guided direct writing: application to fabrication of hepatic-endothelial sinusoid-like structures, Nature Protocols, 1(5):2288-2296(2006)
B. Uygun, A. Soto-Gutierrez, H. Yagi, M.L. Izamis, M.A. Guzzardi, C. Shulman, J. Milwid, N. Kobayashi, A. Tilles, F. Berthiaume, M. Hertl, Y. Nahmias, M.L. Yarmush, K. Uygun. Organ reengineering through development of a transplantable recellularized liver graft using decellularized liver matrix. Nature Medicine. 16(7):814-20. (2010)
> n. a place where an industrial or manufacturing process takes place
In this sense a slaughterhouse or meat processing plant are indeed meat plants. For the primary definition, it also seems plausible to genetically engineer a plant to create animal proteins.